Turnpike properties for a class of piecewise deterministic systems arising in manufacturing flow control

This paper deals with a general class of piecewise deterministic control systems that encompasses FMS flow control models. One uses the Markov renewal decision process formalism to characterize optimal policies via a discrete event dynamic programming approach. A family of control problems with a random stopping time is associated with these optimality conditions. These problems can be reformulated as infinite horizon deterministic control problems. It is then shown how the so-calledturnpike property should hold for these deterministic control problems under classical convexity assumptions. These turnpikes have the same generic properties as the attractors obtained via a problem specific approach in FMS flow control models and production planning and are calledhedging points in this literature.This research has been supported by NSERC-Canada, Grants No. A4952 by FCAR-Québec, Grant No. 88EQ3528, Actions Structurantes, MESS-Québec, Grant No. 6.1/7.4(28), and FNRS-Switzerland.